Polarization beam splitter and optical system using the same, and image displaying apparatus, using the same

ABSTRACT

The polarization beam splitter of the present invention includes a polarized beam splitting layer having a structure in which a plurality of gratings parallel to a first direction are periodically disposed in a second direction orthogonal to the first direction, and of light incident on the polarization beam splitter, light having a chiefly polarized component parallel to the first direction is transmitted therethrough, and light having a chiefly polarized component parallel to the second direction is reflected.

This application is a continuation of application Ser. No. 10/930,128,filed Aug. 31, 2004 (now U.S. Pat. No. 7,116,478), which is incorporatedherein in its entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to a polarization beam splitter used in lights ofa plurality of wavelengths or bands, and relates, for example, tovarious optical apparatuses such as an image taking optical system, aprojection optical system (projector), an image processing apparatus anda semiconductor manufacturing apparatus.

2. Description of Related Art

There is known a polarization beam splitter using dielectric materialmulti-layer film comprising two kinds of media. As shown in FIG. 12 ofthe accompanying drawings, it uses transmission (19) at Brewster's angleregarding P polarized light (18) incident on multi-layer film 17, andeffects reflection (21) by the interference of the multi-layer filmregarding S polarized light (20).

Generally, when the refractive index of the medium on the incidence sidewith an interface as the boundary is defined as n1 and the refractiveindex of the medium on the emergence side is defined as n2, theBrewster's angle θB is given by the following expression (1):tan θB=n2/n1  (1)

It is necessary that this relation is satisfied by a prism medium and aplurality of media forming the dielectric material. Among the refractiveindex np of the prism medium, the refractive index nH of a highrefractive index layer forming the dielectric material and therefractive index nL of a low refractive index layer, it is necessarythat the following relational expression is satisfied.

$\begin{matrix}{n_{P} = \sqrt{\frac{n_{H}^{2}n_{L}^{2}}{\sin^{2}{\theta_{B}\left( {n_{H}^{2} + n_{L}^{2}} \right)}}}} & (2)\end{matrix}$

Regarding the S polarized light, reflecting film by multi-layer filminterference is constituted by the use of the reflectances of the mediumH of the high refractive index layer and the medium L of the lowrefractive index layer. It is possible to realize reflecting film forthe entire area of visible light by 20 to 40 layers. Regarding the Spolarized light, by increasing the number of the layers of the film, itis possible to secure an angle characteristic and a wavelengthcharacteristic widely.

On the other hand, as is disclosed in U.S. Pat. No. 5,042,925, there isknown a polarization beam splitter sandwiching an adhesive agent havingbirefringence, instead of dielectric material multi-layer film, betweenprisms. This uses the refractive index difference of a birefringentmaterial between a normal ray and an abnormal ray, and the refractiveindex difference is not great, but yet by using it at a great incidenceangle of about 60°, one polarized light is selectively totally reflectedto thereby realize polarized light separation.

For total reflection to occur, the incidence angle need be a criticalangle θC or greater, and the critical angle θC is given by the followingexpression:sin θC=n2/n1  (3)

Also, as a polarization beam splitter using sub-wavelength structure(SWS) having a period of a used wavelength or less, there is known oneas shown in FIG. 11 of the accompanying drawings wherein multi-layerfilm is etched into a rectangular grating shape. Here, the wavelengthused is a wavelength supposed to be used in an optical element. When thesupposed wavelength has a band, the wavelength band is defined as a usedwavelength area, and the central wavelength thereof is defined as theused wavelength. For example, in the case of an optical element supposedto be used in visible light, the used wavelength is defined as thecentral wavelength of a visible area even if light incident on theelement includes lights of the other wavelength areas than the visiblearea infrared to ultraviolet. High refractive index layers (H layers) 15of TiO₂ or the like and low refractive index layers (L layers) 16 ofSiO₂ or the like were alternately laminated, and they were etched sothat the ratio of the pitch (period) of periodic structure to the medium(grating width), i.e., a filling factor f, might be about 0.5. Theperiod of the rectangular grating forms structural birefringence asstructure shorter than the wavelength.

In a rectangular grating as shown in FIG. 8A of the accompanyingdrawings wherein a medium 22 of a refractive index n1 and a medium 23 ofa refractive index n2 (in this case, the air between gratings) arerepeated at a ratio of a:b (i.e., the filling factor f=a/(a+b)), when adirection parallel to the grating is defined as TE and a directionorthogonal to the grating is defined as TM, it is known that thestructural birefringence in the direction TE and the direction TM isrepresented by the following expressions (4) and (5), respectively:

$\begin{matrix}{{{TE}\mspace{11mu} n_{TE}} = \sqrt{\frac{{an}_{1}^{2} + {bn}_{2}^{2}}{a + b}}} & (4) \\{{{TM}\mspace{11mu} n_{TM}} = \sqrt{\frac{a + b}{\frac{a}{n_{1}^{2}} + \frac{b}{n_{2}^{2}}}}} & (5)\end{matrix}$

At this time, irrespective of the ratio of a:b, nTE>nTM and therefore,in the direction TE, the refractive index difference between the H layerand the L layer is great, and in the direction TM, the refractive indexdifference between the H layer and the L layer is small. When anappropriate prism medium is adopted, the condition of the Brewster'sangle is satisfied in the direction TM and the P polarized light can betransmitted. The thickness of each layer is independent on the conditionof the Brewster's angle and therefore, by optimizing the filmthicknesses of the H layer and the L layer, it is possible to formdielectric material multi-layer film. Thereby, the S polarized light isreflected and the function as a polarization beam splitter is obtained.This more heightens the degree of selection of a medium satisfying thecondition of the Brewster's angle in P polarized light than apolarization beam splitter constituted by dielectric material thin filmalone. Therefore, at the same time, it is possible to secure thereflectance in the S polarized light high. This leads to the featurethat a polarization beam splitter covering the entire visible light areacan be constituted by the order of 20 layers.

SUMMARY OF THE INVENTION

In the polarization beam splitter using the dielectric materialmulti-layer film, however, the condition of Brewster's angle is used forthe transmission of P polarized light and therefore, the refractiveindices of a prism glass material and the medium of the thin film aresubject to the limitation of expression (2) above and also, it isdifficult to secure an angle characteristic widely. This is not improvedeven if the number of layers is increased.

In a polarization beam splitter with a high molecular material havingbirefringence sandwiched between prisms, the refractive index differenceof the high molecular material between a normal ray and an abnormal rayis not great and therefore, to effect total reflection, the incidenceangle must be about 60° or greater, and this leads to the problem thatthe use of a usable optical system is limited. Also, this element uses ahigh molecular material or the like as a birefringent element and istherefore inferior from the viewpoints of heat resistance and lightresistance.

In the polarization beam splitter of the laminated rectangular gratingtype using SWS, the construction is complicated and the manufacturingcost is high, and the condition of the Brewster's angle is used for thetransmission of P polarized light and therefore, like the dielectricmaterial multi-layer film, it is difficult to obtain a wide anglecharacteristic. Particularly, as is apparent from the structure of thegrating shown in FIG. 11, as the incidence angle becomes great, therefractive index difference between TE and TM becomes null andtherefore, the increase in the reflectance at an incidence angleexceeding the Brewster's angle is greater than when dielectric materialthin film is used, and this hinders widening the angle characteristicand therefore, an element having sufficient performance cannot beobtained.

In order to solve the above-noted problems, the polarization beamsplitter of the present invention is a polarization beam splitter havinga polarized beam splitting layer having structure in which a pluralityof gratings parallel to a first direction are periodically disposed in asecond direction orthogonal to the first direction, and is characterizedin that of light incident on the polarization beam splitter, chieflylight of a polarized component parallel to the first direction istransmitted therethrough and chiefly light of a polarized componentparallel to the second direction is reflected.

Here, it is desirable that for the light of the used wavelength area,the transmittance of the light of the polarized component parallel tothe first direction be 90% or higher, and the reflectance of the lightof the polarized component parallel to the second direction be 90% orhigher. It is desirable that the used wavelength area be a visible lightarea. Of course, light of an ultraviolet wavelength area or light of aninfrared wavelength area may be used.

Here, it is desirable that the plurality of gratings be arranged at aperiod shorter than the used wavelength.

Also, it is desirable that the light of the polarized component parallelto the second direction be reflected by the use of total reflection.

Also, it is desirable that when a surface of the polarization beamsplitter on which a ray is incident is defined as a first surface, andthis first surface and the polarized beam splitting layer are arrangedso as to face each other at an angle which is not parallel, and asurface containing a normal to the first surface and a normal to thepolarized beam splitting layer is defined as a second surface, the firstdirection be substantially parallel to the second surface.

Also, it is desirable that the polarization beam splitter have a shapeof a square pole type having a diamond-shaped bottom surface obtained bytwo transparent members of substantially the same triangle pole shapehaving an isosceles triangle as a bottom surface having had their sidesincluding the bottom sides of their respective isosceles trianglesjoined to each other. It is better if the first direction is disposed soas to be parallel to the diamond-shaped bottom surface.

Also, it is desirable that the material of the plurality of gratings bea dielectric material, and the space between the plurality of gratingsbe filled with air. Here, it is better if the dielectric material istitanium oxide (TiO₂). It is desirable that when of the period at whichthe plurality of gratings are arranged, the rate the dielectric materialoccupies if f, 0.2<f<0.8 . . . (6) be satisfied. Here, it is desirablethat the polarized beam splitting layer be sandwiched between twooptical members. Also, it is desirable that the absolute value of thephotoelasticity constant of the two optical members be smaller than0.1×10⁻⁸ cm²/N. It is desirable that the two optical members have thesame refractive index.

Here, it is better if when the refractive index of the optical membersis defined as nP, and the refractive index of the dielectric material isdefined nG, and of the period at which the plurality of gratings arearranged, the rate the dielectric material occupies is defined as f(filling factor), the following conditional expression is satisfied:

$\begin{matrix}{0.7 < \frac{\sqrt{{fn}_{G}^{2} + 1 - f}}{n_{P}} < 1.3} & (7)\end{matrix}$

Also, it is better if when the refractive index of the optical membersis defined as nP, and the refractive index of the dielectric material isdefined as nG, and of the period at which the plurality of gratings arearranged, the rate the dielectric material occupies is defined as f(filling factor), and the incidence angle of light onto the polarizationbeam splitter is defined as θ, the following conditional expression issatisfied:

$\begin{matrix}{{\sin\;\theta} > \frac{1}{n_{P}\sqrt{\frac{f}{n_{G}^{2}} + 1 - f}}} & (8)\end{matrix}$

Also, it is better if design is made such that a ray is incident on thepolarized beam splitting layer within an angle range including theBrewster's angle determined by the refractive index of the medium of theoptical members and the effective refractive index of the polarized beamsplitting layer for light having a polarized component parallel to thefirst direction.

Also, it is better if the refractive index of the medium of the opticalmembers and the effective refractive index of the polarized beamsplitting layer for the light having the polarized component parallel tothe first direction are made substantially equal to each other.

It is better if the thickness d of the polarized beam splitting layer issuch that the relation thereof with the used wavelength λS on theshortest wavelength side of the light of the used wavelength areasatisfies the following conditional expression:0.5<d/λS  (9)

Also, it is desirable that design be made such that of the lightincident on the polarization beam splitter, chiefly P polarized light isreflected, and chiefly S polarized light is transmitted.

Also, the polarization beam splitter of the present invention has apolarized beam splitting layer having structure in which a plurality ofgratings parallel to a first direction are periodically disposed in asecond direction orthogonal to the first direction, and is characterizedin that of light incident on the polarization beam splitter, chieflylight of a polarized component parallel to the first direction istransmitted, and chiefly light of a polarized component parallel to thesecond direction is reflected.

Here, P polarized light and S polarized light are ordinary names, andpolarized light in which an electric field vibrates in parallel to anincidence flat surface (generally a surface containing an incident rayand a normal to a boundary surface (now the surface of a polarizingelement); in the present case, it is defined as a surface containing anincident ray, a reflected ray and a transmitted ray) is P polarizedlight, and polarized light in which an electric field vibrates in adirection orthogonal to the incidence flat surface is S polarized light.

Also, the image displaying apparatus of this application ischaracterized by at least one display element, an illuminating opticalsystem for illuminating the aforementioned at least one display elementwith light from a light source, and a polarized beam splitting asdescribed above.

Also, it is more desirable that the image display apparatus have aprojection optical system for projecting light from the aforementionedat least one display element onto a projection surface.

Also, it is desirable that the aforementioned at least one displayelement be a reflection type display element. Also, it is better if theaforementioned at least one display element be a plurality of displayelements, and be designed to have a color resolving system forcolor-resolving light from a light source for each wavelength (eachcolor) when it is directed to the plurality of display elements, and acolor combining system for combining reflected lights from the pluralityof display elements. Here, it is more desirable that at least one of thecolor resolving system and the color combining system have the abovepolarization beam splitter. Further, it is better if each of the colorresolving system and the color combining system has at least one ofabove described polarization beam splitter.

According to the present invention as previously described, regardingthe polarization beam splitter, there is the effect that there can berealized a polarization beam splitter which is simple in both ofstructure and design, and yet has a high extinction ratio within wideranges of wavelength characteristic and incidence angle characteristic.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows the construction of a polarization beam splittercorresponding to a first embodiment of the present invention.

FIG. 2 is a typical view of the polarization beam splitter correspondingto the first embodiment of the present invention.

FIGS. 3A and 3B show the construction of the grating shape of thepolarization beam splitter corresponding to the first embodiment of thepresent invention.

FIGS. 4A and 4B show the construction of the grating shape of apolarization beam splitter corresponding to a second embodiment of thepresent invention.

FIG. 5 shows the construction of a polarization beam splittercorresponding to a third embodiment of the present invention.

FIG. 6 shows the construction of a polarization beam splittercorresponding to a fourth embodiment of the present invention.

FIG. 7 shows a construction in which a polarization beam splittercorresponding to a fifth embodiment of the present invention isincorporated into a reflection type liquid crystal projector opticalsystem.

FIGS. 8A and 8B are illustrations of a rectangular type grating of SWS,FIG. 8A illustrating a model of the effective refractive index of therectangular type grating of SWS, and FIG. 8B being a graph representingstructural brefringular type grating of SWS.

FIGS. 9A, 9B and 9C show the polarized beam splitting characteristics ofthe polarization beam splitter according to the first embodiment in thevisible light area by RCWA calculation, FIG. 9A showing the wavelengthcharacteristics of the reflectance of each polarized light at anincidence angle of 42.0°, FIG. 9B showing the wavelength characteristicof the reflectance of each polarized light at an incidence angle of45.0°, and FIG. 9C showing the wavelength characteristic of thereflectance of each polarized light at an incidence angle of 55.0°.

FIGS. 10A, 10B and 10C show polarized beam splitting characteristics ofthe polarization beam splitter according to the second embodiment in thevisible light area by RCWA calculation, FIG. 10A showing the wavelengthcharacteristic of the reflectance of each polarized light at anincidence angle of 37.0°, FIG. 10B showing the wavelength characteristicof the reflectance of each polarized light at an incidence angle of45.0°, and FIG. 10C showing the wavelength characteristic of thereflectance of each polarized light at incidence angle of 50.0°.

FIG. 11 is a typical view of a conventional polarization beam splitterof a multi-layer film etching type.

FIG. 12 is a typical view of a conventional multi-layer filmpolarization beam splitter.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Some embodiments of the present invention will hereinafter be describedwith reference to the drawings.

First Embodiment

FIG. 1 shows the construction of a polarization beam splitter accordingto a first embodiment of the present invention. Tables 1 and 2 belowshow the numerical values of the constructions by Design Examples 1 and2 of a grating of SWS used in this first embodiment.

Referring to FIG. 1, a polarized beam splitting layer is inclined at 45°with respect to the incidence surface of a prism. The grating of SWS, asshown in FIG. 2, is disposed in parallel to the incidence plane, and isdesigned to reflect S polarized light and transmit P polarized lighttherethrough. This grating of SWS adopts such a construction as shown inFIGS. 3A and 3B, and as shown in FIG. 3B, the cross-sectional structureof the grating (a direction parallel to this grating, i.e., a directionperpendicular to the plane of the drawings sheet of FIG. 3B, is referredto as A direction) is of rectangular grating structure (the pitchdirection of this grating, i.e., a direction parallel to the plane ofthe drawing sheet of FIG. 3B is referred to as B direction) in which air24 and TiO² 25 (other medium will also do) are one-dimensionallyalternately repeated, and is of very simple structure in which polarizedlight separation is realized by this single layer alone. Of course, theportion of the grating of TiO² may be formed by laminating a pluralityof different media with respect to the height direction of the grating(i.e., the vertical direction in the plane of the drawing sheet of FIG.3B), and the layer of air may be replaced by other medium than air.

The height of the grating is 700 μm, and sufficiently satisfiesconditional expression (6) for the light of the wavelength in thevisible light area (light of the used wavelength area).

Conditional expression (6) is representative of a condition forcompletely achieving total reflection. Generally it is known that whenlight is incident from a medium of a high refractive index to a mediumof a low refractive index, if the incidence angle thereof is a criticalangle θC or greater, the light is not at all transmitted, but is totallyreflected. At this time, however, light called an evanescent wave oozesin a very minute area near a boundary surface. If there is the followingmedium in the reach area of this light, the light will be transmitted.This phenomenon is attenuated total reflection (ATR), and a conditionalexpression for preventing this ATR is (6).

In the first embodiment, as per Design Example 1 in Table 1, a materialhaving a refractive index as high as about 1.847 is selected as theglass material of the prism, and TiO² having a refractive index as highas about 2.339 is also used as a dielectric material constituting thegrating, and the filling factor of the grating is set to the range ofconditional expressions (7) and (8).

Conditional expression (7) prescribes the condition for the transmissionof a polarized component of A direction to the grating structure, andconditional expression (8) prescribes the condition for the totalreflection of a polarized component of B direction. Here, when TE is thepolarized component of A direction, and TM is the polarized component ofB direction, the refractive indices in the respective directions of thestructural birefringence are given by the aforementioned expressions (4)and (5).

When the refractive index of the optical member is defined as nP and theone-dimensional grating is constituted by a dielectric material nG andair (the refractive index thereof is 1), expressions (4) and (5) areexpressed as (10) and (11), respectively, by the use of the fillingfactor f.

$\begin{matrix}{n_{TE} = \sqrt{{fn}_{G}^{2} + 1 - f}} & (10) \\{n_{TM} = \frac{1}{\sqrt{\frac{f}{n_{G}^{2}} + 1 - f}}} & (11)\end{matrix}$

The Brewster's angle is given by expression (5), and a condition rangeset to expression (10) substituted for the right side of expression (5)is expression (2).

Consequently, expression (2) is the value of tan of the Brewster's angleθB, and prescribes the upper limit and lower limit of this value. If theupper limit and the lower limit are exceeded, that is, if the differencebetween the refractive indices of two media becomes great, reflectanceincreases and the transmission of the polarized component of A directionis hindered.

The total reflection condition is given by expression (7), andexpression (11) substituted for the right side of expression (7) tothereby rearrange it is expression (3).

Consequently, expression (3) is the value of sin of the critical angleθC, and when this value is smaller than the incidence angle, totalreflection occurs in the angle area of the entire light beam.

Thereby, the effective refractive indices of the gratings becomesubstantially the same refractive indices regarding P polarized light,and cause a great refractive index difference regarding S polarizedlight, and the rays of the respective polarized lights are transmittedand totally reflected.

FIGS. 9A to 9C show the result of the simulation of the performance bythe rigorous coupled-wave analysis (RCWA) of this design value. On thelow incidence angle side on which the total reflection condition isdestroyed, the reflectance of S polarized light is lowered, but in theother areas, substantially perfect performance is exhibited.

Conditional expression (6) prescribes the range of f (filling factor),and is a condition for chiefly causing structural birefringenceefficiently. In the grating of SWS as shown in FIG. 8A, the effectiverefractive indices in the respective polarizing directions can be foundby the above-mentioned expressions (4) and (5), and they are graphed inFIG. 8B. As shown, the fact that there is a difference between theeffective refractive indices of TE and TM means having greatbirefringence, but the refractive index difference for f of the media is0 for f=0 and f=1, and is maximum in the vicinity of f=0.5, and it ispreferable that f be equal to or greater than 0.2 and equal to or lessthan 0.7. More preferably, f may be equal to or greater than 0.25 andequal to or less than 0.55. Thus, to select f within the range ofconditional expression (6) is to efficiently utilize the effectiverefractive index.

Second Embodiment

FIGS. 4A and 4B show the grating structure of SWS of a polarization beamsplitter according to a second embodiment of the present invention. InTables 1 and 2 below, there is shown the construction by Design Example2 of the grating of SWS according to the second embodiment. As in thefirst embodiment, a polarized beam splitting layer is inclined at 45°with respect to the incidence surface of the prism, and is designed toreflect S polarized light and transmit P polarized light therethrough.The cross-sectional structure of the grating is rectangular gratingstructure in which air and TiO₂ are alternately repeated. As shown inTable 2, it is structure satisfying conditional expressions (7) and (8).In the second embodiment, f is set so as to become a value approximateto the lower limit of the condition of expression (7), whereby regardingthe total reflection of expression (8), the angle characteristic can beset widely on the short wavelength side.

FIGS. 10A-10C show the result of the simulation of the performance byRCWA of this design value. The total reflection condition widens on thelow incidence angle side. In exchange for it, the reflectance of Ppolarized light is high on the high incidence angle side.

Third Embodiment

FIG. 5 shows the construction of a polarization beam splitter prismaccording to a third embodiment of the present invention. Thepolarization beam splitter of Design Example shown in Table 1 and Table2 is inserted in the prism inclined into a diamond shape. Incident lightfrom the left side of FIG. 5 is incident on a prism surfaceperpendicularly thereto, and is incident on the polarization beamsplitter at an angle greater than 45°. Regarding the light being totallyreflected, a greater incidence angle is more advantageous, but the prismis inclined into a diamond shape at about 10° as described above,whereby the incidence angle can be changed by 5°.

Fourth Embodiment

FIG. 6 shows the construction of a polarization beam splitter prismaccording to a fourth embodiment of the present invention. Thepolarization beam splitter of Design Example 1 is inserted in a prism of45°. The direction of the grating is orthogonal to the incidence plane.This embodiment is one in which the transmission and reflection ofpolarized lights to be separated which cannot be realized by apolarization beam splitter of multi-layer film using the ordinaryBrewster's angle are made converse. It is possible to control thedirection in which light is to be directed and the direction ofpolarization.

Fifth Embodiment

FIG. 7 shows a reflection type image modulating apparatus using thepolarization beam splitter of the present invention which is a fifthembodiment of the present invention. In FIG. 7, the reference numeral 1designates a light source comprising a high pressure mercury lamp or thelike, the reference numeral 2 denotes a reflector for radiating lightfrom the light source 1 in a predetermined direction, the referencenumeral 3 designates an integrator for forming an illuminating areahaving uniform illuminating intensity, and comprised of fly-eye lenses 3a and 3 b, the reference numerals 4 a, 4 b and 4 c denote a polarizedlight converting element for converting non-polarized light into apredetermined linearly polarized light (making it uniform in apolarizing direction), the reference numeral 5 designates a condenserlens for condensing the illuminating light, the reference numeral 6denotes a mirror, the reference numeral 7 designates a field lens formaking the illuminating light into telecentric light, the referencenumeral 8 denotes a dichroic mirror for transmitting green wavelengtharea light therethrough, and the reference characters 9 a, 9 b and 9 cdesignate polarized beam splitting prisms having gratings 9 a 1, 9 b 1and 9 c 1 of polarized beam splitting SWS, and the gratings 9 a 1, 9 b 1and 9 c 1 of this SWS are the gratings of polarized beam splitting SWSof Design Example 1 or Design Example 2 in Table 1 and Table 2, and havethe characteristic of reflecting S polarized light and transmitting Ppolarized light therethrough. The reference characters 10 a and 10 bdenote color selective phase difference plates for changing (rotating)the polarizing directions of lights of predetermined wavelength areas by90°, the reference characters 11 r, 11 g and 11 b designate reflectiontype liquid crystal display elements for reflecting the incidentilluminating light and also, modulating it in conformity with an imagesignal and forming image light, the reference characters 12 r, 12 g and12 b denote quarter phase difference plates, and the reference numeral14 designates a projection lens system (which may include a mirror ormay be comprised of mirror alone).

If as in the above-described construction, use is made of a polarizationbeam splitter having the grating structure of SWS, there can be realizeda reflection type liquid crystal projector which is excellent in theincidence angle characteristic and the wavelength characteristic and istherefore capable of projecting an image of very high contrast.

TABLE 1 Refractive Layer Refractive Index of Thick- Grating IndexGrating Grating f(Filling ness Pitch of Prism Medium Medium Factor) (nm)(nm) Design 1.847 TiO2 2.339 0.4 700 120 Example 1 Design 1.901 TiO22.339 0.3 700 120 Example 2

TABLE 2 Refractive Refractive Index n Index n Value of Value ofRefractive in TE in TM Conditional Conditional Brewster's Index ofdirection direction Expression Expression Angle Critical Prism TE TM (2)(3) θ_(B) Angle θ_(C) Design 1.847 1.67 1.219 0.904 0.66 64.7 33.4Example 1 Design 1.901 1.53 1.151 0.805 0.605 38.8 31.2 Example 2

This application claims priority from Japanese Patent Application No.2003-308787 filed Sep. 1, 2003, which is hereby incorporated byreference herein.

1. A polarization beam splitter having: a polarized beam splitting layerhaving a structure in which a plurality of gratings parallel to a firstdirection are periodically disposed in a second direction orthogonal tothe first direction, each of the gratings having a refractive index; andtwo optical members sandwiching therebetween the polarized beamsplitting layer, each of the members having a refractive index of whichrefractive indices are equal to each other, when the refractive indicesof the optical members is defined as nP, and the refractive index of thegratings is defined as nG, and a value obtained by dividing a width ofthe gratings by a disposing period is defined as f, and an incidentangle of light incident into the polarization beam splitter is definedas θ, the following conditional expression is satisfied${{\sin\;\theta}\; > \frac{\square}{n_{p}\sqrt{\frac{f}{n_{G}^{2}} + 1 - f}}},$wherein the light of the polarized component parallel to said seconddirection is reflected by the use of total reflection.
 2. The polarizedbeam splitter according to claim 1, wherein for light of a usedwavelength area, the transmittance of the light of the polarizedcomponent parallel to said first direction is 90% or greater, and thereflectance of the light of the polarized component parallel to saidsecond direction is 90% or greater.
 3. The polarization beam splitteraccording to claim 1, wherein said used wavelength area is a visiblelight area.
 4. The polarization beam splitter according to claim 1,wherein said plurality of gratings are arranged at a period shorter thanthe used wavelength.
 5. The polarization beam splitter according toclaim 1, wherein when a surface of said polarization beam splitter onwhich a ray is incident is defined as a first surface, and said firstsurface and the polarized beam splitting layer are disposed so as toface each other at an angle which is not parallel, and a surfacecontaining a normal to said first surface and a normal to said polarizedbeam splitting layer is defined as a second surface, said firstdirection is substantially parallel to said second surface.
 6. Thepolarization beam splitter according to claim 1, which has a shape of asquare pole type having a diamond-shaped bottom surface obtained by twotransparent members of triangle poles of the substantially the sameshape having isosceles triangles as bottom surfaces having their sidesincluding the bottom sides of the respective isosceles triangles joinedto each other.
 7. The polarization beam splitter according to claim 6,which is disposed so that said first direction may be parallel to saiddiamond-shaped bottom surface.
 8. The polarization beam splitteraccording to claim 1, wherein when a value obtained by dividing thewidth of said gratings by said period is defined as f, 0.2<f<0.8 issatisfied.
 9. The polarization beam splitter according to claim 1,wherein said polarized beam splitting layer is sandwiched between twooptical members, and the absolute value of the photoelasticity constantsof said two optical members is smaller than 0.1×10⁻⁸ cm²/N.
 10. Thepolarization beam splitter according to claim 1, wherein said polarizedbeam splitting layer is sandwiched between two optical members, and therefractive indices of said two optical members are equal to each other.11. The polarization beam splitter according to claim 10, wherein whenthe refractive index of said optical members is defined as nP, and therefractive index of said gratings is defined as nG, and a value obtainedby dividing the width of said gratings by said period is defined as f,the following conditional expression is satisfied:$0.7 < \frac{\sqrt{{fn}_{G}^{2} + 1 - f}}{n_{P}} < {1.3.}$
 12. Thepolarization beam splitter according to claim 1, wherein said polarizedbeam splitting layer is sandwiched between two optical members, and aray is incident on said polarized beam splitting layer within an anglerange including Brewster's angle determined by the refractive index ofthe media of said optical members and the effective refractive index ofsaid polarized beam splitting layer for the light having the polarizedcomponent parallel to said first direction.
 13. The polarization beamsplitter according to claim 1, wherein said polarized beam splittinglayer is sandwiched between two optical members, and the refractiveindex of the media of said optical members and the effective refractiveindex of said polarized beam splitting layer for the light having thepolarized component parallel to said first direction are substantiallyequal to each other.
 14. The polarization beam splitter according toclaim 1, wherein the thickness d of said polarized beam splitting layeris such that the relation thereof with a wavelength XS on the shortestwavelength side of light of a used wavelength area satisfies thefollowing condition:0.5<d/λS.
 15. An image displaying apparatus comprising: a displayelement; and an illumination optical system comprising the polarizationbeam splitter according to claim 1, for illuminating the display elementwith light from a light source.
 16. A polarization beam splitter having:a polarized beam splitting layer having a structure in which a pluralityof gratings parallel to a first direction are periodically disposed in asecond direction orthogonal to the first direction, each of the gratingshaving a refractive index; and two optical members sandwichingtherebetween the polarized beam splitting layer, each of the membershaving a refractive index of which refractive indices are equal to eachother, when the refractive indices of the optical members is defined asnP, and the refractive index of the gratings is defined as nG, and avalue obtained by dividing a width of the gratings by a disposing periodis defined as f, and an incident angle of light incident into thepolarization beam splitter is defined as θ, the following conditionalexpression is satisfied${{\sin\;\theta}\; > \frac{1}{n_{p}\sqrt{\frac{f}{n_{G}^{2}} + 1 - f}}},$wherein for light of a used wavelength area, the transmittance of thelight of the polarized component parallel to said first direction is 90%or greater, and the reflectance of the light of the polarized componentparallel to said second direction is 90% or greater.
 17. An imagedisplaying apparatus comprising: a display element; and an illuminationoptical system comprising the polarization beam splitter according toclaim 16, for illuminating the display element with light from a lightsource.